I played professionally while driving a Camry! A 20” kick drum and a mic for it is all you need, and that fits in the back seat of a Camry. Everything else can go in the trunk, at least with a reasonably-sized kit.
One thing to note is that "big car" is not a universal classifier. To a Canadian or American, Camry is not a big car. To many Europeans, Camry is a mind boggingly MASSIVE car :->